3. Suppose L : R² → R² is a linear transformation.(a) If L(ej) = e + €2 and L(e,)that e, + e, is an eigenvector of L. Find thecorresponding eigenvalue.= e1 + e2, verify(b) Find the characteristic polynomial of L andthen find another eigenvalue of L.(c) Find an eigenvector for the second eigenvalueyou found in part (b).

Answered: Image /qna-images/answer/2e95a4fb-a233-4539-ac67-6a1b000c032b.jpg

3. Suppose L : R² → R² is a linear transformation. (a) If L(ej) = e + €2 and L(e,) = e¡ + e2, verify that e, + e, is an eigenvector of L. Find the corresponding eigenvalue. (b) Find the characteristic polynomial of L and then find another eigenvalue of L. (c) Find an eigenvector for the second eigenvalue you found in part (b).

3. Suppose L : R² → R² is a linear transformation. (a) If L(ej) = e + €2 and L(e,) = e¡ + e2, verify that e, + e, is an eigenvector of L. Find the corresponding eigenvalue. (b) Find the characteristic polynomial of L and then find another eigenvalue of L. (c) Find an eigenvector for the second eigenvalue you found in part (b).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices

Problem 28EQ

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